Hierarchy in mathematics: preliminary thoughts

J’ai glissé dans cette moitié du monde, pour laquelle l’autre n’est qu’un décor.

Annie Ernaux

“Who the hell is Annie Ernaux, and why did this disorganized snob of an author include a quotation from this obscure figure in a language I don’t understand?”  That’s the kind of question you are likely to ask if you are the sort of reviewer who boasts of never having read Max Weber, or if you are the sort of reader who devotes his spare time to making snide remarks on Google+.  The above quotation is placed as the epigraph to Chapter 2 of MWA, entitled “How I acquired charisma.”  Some readers, including the two authorities just cited, have read that chapter as a celebration of the hierarchical structure of mathematics and a self-celebration of the author’s place in that hierarchy.  No one is going to outlaw snide comments on social media, and I’m grateful for that; but it does seem to me that a reviewer’s responsibilities includes making an effort to become reasonably well-informed about the contents of the book under review.  Modern technology makes this really easy.  A reviewer who doesn’t read French can submit that quotation to the indignities of Google Translate, and this is what comes out:

I slipped in that half of the world, for which the other is only a decoration.

The translation isn’t perfect, but if you replace “in” by “into” it makes more sense:


I slipped into that half of the world, for which the other is only a decoration.

It’s now natural for the reviewer to wonder:  is this Annie Ernaux just one of those self-celebratory French snobs, like Marie Antoinette?    Wikipedia has the answer to that question too.  Not the English Wikipedia, unfortunately, and the reviewer will have to show a bit more initiative, looking up her biographical details on her French Wikipedia (or Wikipédia) page, (with the help of some automatic translator, if necessary), to try to understand what the author of MWA may have been trying to communicate by choosing this quotation to open a chapter that largely focuses on the hierarchical structure of mathematics.

I’ll get to the answer in the next paragraph, but first I should explain that I have been thinking about mathematical hierarchy again after I returned to the liberated mathematician Piper Harron’s blog entry on “Why I do not talk about math,” and especially the discussion that ensued.  I will soon be writing a post largely devoted one of Harron’s sentences, and how it relates to the subject of Chapter 2:

My experience discussing math with mathematicians is that I get dragged into a perspective that includes a hierarchy of knowledge that says some information is trivial, some ideas are “stupid”; that declares what is basic knowledge, and presents open incredulity in the face of dissent.

But first, before I return to Annie Ernaux, I should explain that the writing of Chapter 2 began with the following sentence, that finally found its place in the last paragraph, and that has the same meaning as the first half of the epigraph from Ernaux:

My friend’s point was that even my modest level of charisma entitles me not only to say in public whatever nonsense comes into my head … but even to get it published.

This is a slight exaggeration, but it is not intended as irony.  It rather serves as the starting point for reflections on the social institution of pure mathematics in which the authority to speak for the subject is distributed according to a relatively rigid charismatic hierarchy, a situation already identified by Bourdieu and Passeron, though not specifically with regard to mathematics, in the quotation that immediately follows in MWA:

Or, to quote Pierre Bourdieu and Jean-Claude Passeron, “There is nothing upon which [the charismatic professor] cannot hold forth… because his situation, his person, and his rank ‘neutralize’ his remarks.”

Annie Ernaux belongs to a current among French writers strongly influenced by Bourdieu, who made a film called Sociology is a Combat Sport.  Younger authors in this current include Didier Eribon and Edouard Louis.   Ernaux’s French Wikipedia article makes her debt to Bourdieu explicit, and I will quote it in detail:

L’œuvre d’Annie Ernaux est très fortement marquée par une démarche sociologique14 qui tente de « retrouver la mémoire de la mémoire collective dans une mémoire individuelle15 ». En tentant d’échapper au « piège de l’individualité », l’œuvre d’Ernaux esquisse une redéfinition de l’autobiographie, selon laquelle « l’intime est encore et toujours du social, parce qu’un moi pur, où les autres, les lois, l’histoire, ne seraient pas présents est inconcevable16. »

Dès lors, Annie Ernaux adopte une démarche objectivante empruntée au sociologue, et se considère avant tout comme la somme d’un vécu nourri de références et de caractéristiques collectives :

« Je me considère très peu comme un être singulier, au sens d’absolument singulier, mais comme une somme d’expérience, de déterminations aussi, sociales, historiques, sexuelles, de langages, et continuellement en dialogue avec le monde (passé et présent), le tout formant, oui, forcément, une subjectivité unique. Mais je me sers de ma subjectivité pour retrouver, dévoiler les mécanismes ou des phénomènes plus généraux, collectifs17. »

Selon elle, cette démarche sociologisante permet d’élargir le « je » autobiographique traditionnel : « Le « Je » que j’utilise me semble une forme impersonnelle, à peine sexuée, quelquefois même plus une parole de « l’autre » qu’une parole de « moi » : une forme transpersonnelle en somme. Il ne constitue pas un moyen de m’autofictionner, mais de saisir, dans mon expérience, les signes d’une réalité18. »

Ainsi, ses ouvrages traitent du « métissage social », de sa trajectoire (fille de petits commerçants devenue étudiante, professeure puis écrivain) et des mécanismes sociologiques qui l’accompagnent.

Lors du décès du sociologue Pierre Bourdieu en 2002, Annie Ernaux signe un texte-hommage publié dans Le Monde19, dans lequel elle revient sur les liens ténus qui unissent son œuvre à la démarche sociologique, les textes de Bourdieu ayant été pour elle « synonymes de libération et de « raisons d’agir » dans le monde ». En 2013, elle participe à l’ouvrage collectif Pierre Bourdieu. L’insoumission en héritage, dans lequel elle écrit l’article « La Distinction, œuvre totale et révolutionnaire »20, sur l’essai du sociologue : La Distinction. Critique sociale du jugement, publié en 1979.

The passages in (my) boldface express exactly what I mean in MWA by treating my experience as “ideal-typical”; here are Google’s translations of the passages, corrected:

I make use of my subjectivity to locate or uncover mechanisms or more general, collective, phenomena.

The ‘I’ that I use seems an impersonal form …sometimes more a word belonging to the “other” rather than a word belonging to “me”: transpersonal, in short. It does not constitute a means of fictionalizing myself, but rather to grasp, through my experience, the signs of a reality.

Much of Bourdieu’s most influential work, notably the book cited at the end of the Wikipedia excerpt, deals with the ways class differences are expressed by means of distinctive signs of taste.  The authors mentioned above (Eribon, Louis, and Ernaux, and no doubt many others I have not read) have at least one thing in common with one another, and with Bourdieu — they all grew up in “modest” circumstances, were identified as talented students, learned the signs of distinction, and “slipped into [the other] half of the world” with a clear vision of the mechanisms of the charismatic hierarchy into which they had advanced, and a vision no less clear of what they had left behind.

The rest of the explication of the epigraph is left to the reader as an exercise.


4 thoughts on “Hierarchy in mathematics: preliminary thoughts

  1. Voynich

    Just an obvious thought: in mathematics, the people who get charisma are (99% of the time) exactly the people with a history of having ideas which are “good” or which “stick” somehow. If charisma means being able to spout off about whatever, aren’t those exactly the people who deserve the right to spout off? To use Bourdieu and Passeron’s term, It’s not merely rank which neutralizes their remarks, it’s rank obtained as a consequence of a history of making good remarks! Seems reasonable to me.


    1. mathematicswithoutapologies Post author

      One point is that the people who have good mathematical ideas are not necessarily qualified (professionally or otherwise) to write books about mathematics. I can mention some recent examples, but perhaps the subject of this post from last year is the most striking illustration of the problem.

      One of the points I’m going to make, eventually, when I get around to finishing the list of what is wrong with MWA, is that it relies too heavily on quotations from great (mostly) men; in other words, that it reproduces the hierarchy in its choice of sources.


  2. Pingback: Mathematical prizes and the “oppressive hierarchy” | Mathematics without Apologies, by Michael Harris

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